The rationals are a field.

Field exercises.

The rationals are gappy.

Backstitching the proof.

Another characterization, by lack of suprema.

Partial orders.

Poset exercises.

Intervals.

Strict partial orders.

Bounds.

Bound theorems.

Suprema.

Suprema 2.

Total orders.

Total order theorem.

Ordered fields.

Ordered field theorems.

Ordered field theorems 2.

Ordered field theorems 3.

Ordered field theorems 4.